Factorisation d'opérateurs aléatoires, d'après Benyamini et Gordon
Factorizable matrices
We study square matrices which are products of simpler factors with the property that any ordering of the factors yields a matrix cospectral with the given matrix. The results generalize those obtained previously by the authors.
Factorization of CP-rank- completely positive matrices
A symmetric positive semi-definite matrix is called completely positive if there exists a matrix with nonnegative entries such that . If is such a matrix with a minimal number of columns, then is called the cp-rank of . In this paper we develop a finite and exact algorithm to factorize any matrix of cp-rank . Failure of this algorithm implies that does not have cp-rank . Our motivation stems from the question if there exist three nonnegative polynomials of degree at most four that...
Factorization of matrices associated with classes of arithmetical functions
Let f be an arithmetical function. A set S = x₁,..., xₙ of n distinct positive integers is called multiple closed if y ∈ S whenever x|y|lcm(S) for any x ∈ S, where lcm(S) is the least common multiple of all elements in S. We show that for any multiple closed set S and for any divisor chain S (i.e. x₁|...|xₙ), if f is a completely multiplicative function such that (f*μ)(d) is a nonzero integer whenever d|lcm(S), then the matrix having f evaluated at the greatest common divisor of and as its...
Factorizations for q-Pascal matrices of two variables
In this second article on q-Pascal matrices, we show how the previous factorizations by the summation matrices and the so-called q-unit matrices extend in a natural way to produce q-analogues of Pascal matrices of two variables by Z. Zhang and M. Liu as follows [...] We also find two different matrix products for [...]
Fast Givens transformation for quaternion valued matrices applied to Hessenberg reductions.
Fermat's Equation in Matrices
The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.
Fermat's theorem for matrices revisited
Fine spectra of tridiagonal symmetric matrices.
Finite dimensional projection constants
First order linear ordinary differential equations in associative algebras.
Fluctuations de la loi empirique de grandes matrices aléatoires
Focal power.
Formes quadratiques réelles semi-définies. Démonstration élémentaire du critère des mineurs principaux.
Fredholm determinants
The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.
Free generalized gamma convolutions.